(Q13)Find the roots of the following quadratic equation, if they exist by the method of completing the square.

(ii) 4x2 +4√ 3x + 3 = 0

Answer:

Given: 4x2 + 4√ 3x + 3 = 0

4x2 + 4√3x = -3

(2x)2 + 2(2x)√3 = -3

LHS is of the form a2 + 2ab where b = √3

∴ Adding b2 = (√3)2 = 3 on both sides, we get

(2x)2 + 2(2x)(√3) + (√3)2 = -3 + (√3)2

(x +√)2 = -3 + 3 = 0

(x +√)2 = 0

(x +√) = 0

x = -√

x =
-√
∴ The roots are
-√
 ,
-√
 .